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Procedia Engineering 29 (2012) 861 865

1877-7058 2011 Published by Elsevier Ltd.

doi:10.1016/j.proeng.2012.01.055

Available online at www.sciencedirect.com

2012 International Workshop on Information and Electronics Engineering (IWIEE)

The FPGA Implementation of Color Gamut Conversion in

Laser Display

Bailin Na**, Yingying Wu,Weisheng Wang

School of Information Science and Technology, East China Normal University, 500 Dongchuan Road, Shanghai, China

Abstract

Because of the lasers larger colour gamut, the images played by the laser display will be more vivid and more

colourful, but the most standard signals are coding by the formats which have small gamut, so sometimes the images

displayed by the laser may have the phenomenon of colour deviation and colour confusion. The paper proposes a

system to solve the problem, and implement the system on FPGA platform.

2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Harbin University

of Science and Technology.

Keyword: LCH, Tetrahedral interpolation, Gamut mapping, LLIN, FPGA, chromaticity coordinate

1. Introduction

Now the Laser display technology arouses widespread interests as a new generation of display

technology, because of its large gamut display which can be watched by human eyes, colour saturation,

the larger display size and flexible variable, and free of harmful electromagnetic radiation, etc. In recent

years, people pay more attentions on the Laser display technology, as that the sizes of the solid-state

lasers become smaller and the power of the solid-state lasers become more powerful. The colours of red,

green and blue solid state laser (DPL) are used as the primary colours in Solid-state laser video display

technology.

As the formats which are used for the TV signal are different, the coding and the chromaticity

coordinates of the three primary colors are different too. No matter which format is chosen, after

decoding, the intensity modulation signal of the three colors RGB could be gotten. But the chromaticity

** Corresponding author. smartfour@126.com

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coordinates are different between the laser and the others, the color reproduction ranges are also different.

So the images reproduced by laser will have the phenomenon of color deviation and color confusion.

Therefore, to achieve the images reproduced by laser correctly, the color conversion formula must be

established from the existing standard measure of RGB to the Laser measure of RGB. Then depth image

can be established. Wavelet analysis algorithms are generally complex and difficult to implement in

FPGA. This paper proposes a new method to implement wavelet analysis on images real-time in FPGA

for the depth images.

2. Color space conversion

Color space conversion is used to solve the problem that the chromaticity coordinate system of the

device is different with each other, so in order to achieve that, an intermediate color space should be

needed to link different devices. A uniform color space is chose as the standard space. The color space

requires a large enough color gamut so when the conversions are making, there are no data lost. The color

space should also be device-independent space.

Fig.1 The color gamut of different formats. The largest green triangle is the color gamut of LASER.

This paper uses the LCH color space as the conversional space, the intermediate color space. The LCH

color space is color-opponent space with dimension L for lightness and C for color saturation and H for

color hue, based on nonlinearly compressed CIE XYZ color space coordinates. Color space conversion

processing from RGB to LCH involves three steps: (1) RGB to XYZ; (2) XYZ to Lab ;( 3) Lab to LCH.

Conversion Formula:

X

Y

r r g g b b

r r g g b b

r r g g b b

C x R C x G C x B

C y R C y G C y B

Z C z R C z G C z B

= + +

= + +

= + +

While,

1

/

1

/

r g b n nr

g r g b

n nb r g b

x x x x yC

C y y y

z yC z z z

=

(1)

Among,r g b

C C C

are matching component factors of RGB, r r rx y z

are chromaticity coordinates of R (Thelaser), g g gx y z are chromaticity coordinates of G, and b b bx y z are chromaticity coordinates of B.

* 1/3

0

* 1/3 1/3

0 0

* 1/3 1/3

0 0

116( / ) 16

500[( / ) ( / ) ]

200[( / ) ( / ) ]

L Y Y

a X X Y Y

b Y Y Z Z

=

=

=

(2)

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863Bailin Na et al. / Procedia Engineering 29 (2012) 861 865

* 1/3

0

* * 2 * 2 1/2

* * *

116( / ) 16

[( ) ( ) ]

(180 / )arctan(( ) / ( ))

L Y Y

C a b

H b a

=

= + =

(3)

While, 0/ 0.01Y Y >The first step, the conversion from RGB space to XYZ space requires a 3*3 matrix, such as Formula (1)

figures, this step need linear operations, so it can be implemented in hardware easily. But the second andthird steps are both nonlinear operation, they cant be implemented in real-time. This paper proposed a

new method building a lookup table to simplify the process from XYZ to LAB to LCH. The method can

reduce computational complexity while increasing processing speed.

3. Tetrahedral interpolation

Tetrahedron is the smallest of the three-dimensional can not be divided; if one pixel point falls inside a

tetrahedron, you can use the four vertices of the tetrahedron correspond the value of the pixel point.

Fig.2. The different type of the tetrahedral interpolation. (a) is the tradition type, and (b) is the innovative type.

The four vertices of the tetrahedron are the P1, P2, P3, P4, and the volume is V. When the

interpolation point P falls inside the tetrahedron, P point and the four vertices compose the other four sub-

tetrahedrons. The volume of each sub-tetrahedron is Vi.4

1

F( ) ( )*( / )i i

i

p F p V V=

= (4)

In this method, only the four vertices are used for interpolation. The reductions of interpolation points

make the computational complexity reduction. Only 4 multiplications and 3 additions are needed. The

key of Tetrahedral interpolation is that how to decide the four vertices, to make the chromatism CHE as

small as possible.

2 2 2CHE = ( ) ( ) ( H)L C + + (5)

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The first step is that the sampling points should be set up. This paper take the high-three of every rgb

component as MSB (most significant bits), low-five as the LSB (least significant bits).So there are 32

gray-levels between every sampling points.Fig2.(b) is the map of Sampling Points. The polyhedron

illustrated by Fig2.(b) indicates 7 sampling points, one in middle and the other six in vertex. To make the

interpolation, which area the P in should be estimated by using Formula (6) firstly, and then the P1, P2,

P3, P4 could be gotten. There are 8 tetrahedral in the polyhedron.

* * / 2 * / 2 *

* * / 2 * / 2 *

* * / 2 * / 2 *

r r

g g

b b

l a P l a l or l a l P l a

l b P l b l or l b l P l b

l c P l c l or l c l P l c

+